Nuprl Lemma : fpf-dom-compose
∀[x:Top]. ∀[f:a:Top fp-> Top]. ∀[g,eq:Top].  (x ∈ dom(g o f) ~ x ∈ dom(f))
Proof
Definitions occuring in Statement : 
fpf-compose: g o f
, 
fpf-dom: x ∈ dom(f)
, 
fpf: a:A fp-> B[a]
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
top: Top
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
fpf_dom_compose_lemma, 
top_wf, 
fpf_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
sqequalTransitivity, 
computationStep, 
dependent_functionElimination, 
thin, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesis, 
isect_memberFormation, 
introduction, 
sqequalAxiom, 
isectElimination, 
hypothesisEquality, 
because_Cache, 
lambdaEquality
Latex:
\mforall{}[x:Top].  \mforall{}[f:a:Top  fp->  Top].  \mforall{}[g,eq:Top].    (x  \mmember{}  dom(g  o  f)  \msim{}  x  \mmember{}  dom(f))
Date html generated:
2018_05_21-PM-09_27_44
Last ObjectModification:
2018_02_09-AM-10_23_17
Theory : finite!partial!functions
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